TITLE

On the Best Approximation by Ridge Functions in the Uniform Norm

AUTHOR(S)
Gordon, Y.; Maiorov, V.; Meyer, M.; Reisner, S.
PUB. DATE
January 2002
SOURCE
Constructive Approximation;2002, Vol. 18 Issue 1, p61
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
We consider the best approximation of some function classes by the manifold M[SUBn] consisting of sums of n arbitrary ridge functions. It is proved that the deviation of the Sobolev class W[SUPr,d,SUPp] from the manifold M[SUBn] in the space L[SUBq] for any 2 = q = p = 8 behaves asymptotically as n[SUP-r/(d-1)]. In particular, we obtain this asymptotic estimate for the uniform norm p = q = 8.
ACCESSION #
8871420

 

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